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Keynes Meets Markowitz: the Trade-Off Between Familiarity and Diversification

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Keynes Meets Markowitz: the Trade-Off Between Familiarity and Diversification Keynes Meets Markowitz: The Trade-off Between Familiarity and Diversification January 2011 Phelim Boyle, Wilfrid Laurier University Lorenzo Garlappi, University of British Columbia Raman Uppal, EDHEC Business School Tan Wang, University of British Columbia Abstract We develop a model of portfolio choice that nests the views of Keynes—who advocates concentration in a few familiar assets—and Markowitz—who advocates diversification across assets. We rely on the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor's "familiarity" toward assets. The model shows that when an investor is equally ambiguous about all assets, then the optimal portfolio corresponds to Markowitz's fully-diversied portfolio. In contrast, when an investor exhibits different degrees of familiarity across assets, the optimal portfolio depends on (i) the relative degree of ambiguity across assets, and (ii) the standard deviation of the estimate of expected return on each asset. If the standard deviation of the expected return estimate and the difference between the ambiguity about familiar and unfamiliar assets are low, then the optimal portfolio is composed of a mix of both familiar and unfamiliar assets; moreover, an increase in correlation between assets causes an investor to increase concentration in the assets with which they are familiar (flight to familiarity). Alternatively, if the standard deviation of the expected return estimate and the difference in the ambiguity of familiar and unfamiliar assets are high, then the optimal portfolio contains only the familiar asset(s) as Keynes would have advocated. In the extreme case in which the ambiguity about all assets and the standard deviation of the estimated mean are high, then no risky asset is held (non-participation). The model also has empirically testable implications for comparative statics with respect to idiosyncratic and systematic risk: in response to a change in idiosyncratic risk, the Keynesian portfolio always exhibits a bigger change than the Markowitz portfolio, while the opposite is true for a change in systematic risk. Keywords: Investment, portfolio choice, ambiguity, robust control, underdiversification. JEL Classication: G11, G12, G23, D81 We gratefully acknowledge financial support from Inquire-UK and Inquire-Europe; however, this article represents the views of the authors and not of Inquire. We would also like to thank the following for comments: Ron Anderson, Suleyman Basak, Bruno Biais, Victor DeMiguel, David Feldman, Francisco Gomes, Juan-Pedro Gomez, Phillip Illeditisch, Dietmar Leisen, Sujoy Mukerji, Vasant Naik, Anthony Neuberger, Loriana Pelizzon, Valery Polkovnichenko, Stijn Van Nieuwerburgh, Dimitri Vayanos, Laura Veldkamp, JohanWalden, Hongjun Yan, Xunyu Zhou, and participants at seminars given at EDHEC Business School, London Business School, McGill University, Northwestern University, Oxford University, Tilburg University, University of Toronto, University of Venice, Wilfrid Laurier University, the Oxford-Man conference on Robust Techniques in Quantitative Finance, the joint conference of INQUIRE-UK and INQUIRE-Europe, the Nordic Finance Network (NFN) Research Workshop, the meetings of the European Finance Association, and the meetings of the American Finance Association. EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty and the privileged relationship with professionals that the school has cultivated since its establishment in 1906. EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore focused its research on themes that satisfy the needs of professionals. EDHEC pursues an active research policy in the field of finance. EDHEC-Risk Institute carries out numerous research programmes in the areas of asset allocation and risk management in both the 2 traditional and alternative investment universes. Copyright © 2012 EDHEC 1. Introduction John Maynard Keynes and Harry Markowitz personify two contrasting schools of thought regarding the process of portfolio selection. On the one hand, Keynes advocates allocating wealth in the few stocks about which one feels most favorably: The right method in investment is to put fairly large sums into enterprises which one thinks one knows something about [. ]. It is a mistake to think that one limits one's risk by spreading too much between enterprises about which one knows little and has no reason for special confidence. [. ] One's knowledge and experience are definitely limited and there are seldom more than two or three enterprises at any given time in which I personally feel myself entitled to put full confidence.1 Keynes is not alone in his view on portfolio selection. Loeb (1950), for example, advocates: "Once you obtain confidence, diversification is undesirable; diversification [is] an admission of not knowing what to do and an effort to strike an average." Moreover, the Keynesian view is far from old-fashioned: Warren Buffett, in his letter to the Berkshire Hathaway shareholders in 1991, espouses the same view and supports it by citing the above quote from Keynes.2 On the other hand, Markowitz (1952, p. 77), championing the concept of diversification, argues that it is inefficient to put a large holding in just a few stocks, and that an investor should instead diversify across a large number of stocks, as the following quote effectively summarizes: Diversification is both observed and sensible; a rule of behavior which does not imply the superiority of diversification must be rejected both as a hypothesis and as a maxim. Even though Markowitz's idea of diversification has been accepted as one of the most fundamental tenets of modern financial economics, a vast body of empirical evidence that we review below suggests that investors do not hold diversified portfolios but rather invest heavily in only a few assets, as suggested by Keynes. However, because of the lack of an analytical characterization, the academic literature has so far paid relatively little attention to Keynes's view on portfolio selection, preferring instead the more extensively developed analytical framework supporting Markowitz's idea of diversification. Our objective in this paper is to ll this gap by developing a model that allows us to assess, both qualitatively and quantitatively, the different trade-offs advocated by Keynes and Markowitz.3 In particular, our goal is to understand the implications of Keynes's view for the portfolios selected by individual investors, and to answer the following questions. Under what circumstances should investors hold only the assets they "feel confident about" (familiar assets), and when should they hold only the broadly diversified (and possibly unfamiliar) market portfolio? When they hold both, how should their portfolio be allocated between the familiar asset(s) and the market portfolio? How does this allocation depend on the volatility and correlation of asset returns? When the number of assets available for investment is large, are the benefits of investing in the familiar assets overwhelmed by the benefits from diversification? We model the lack of familiarity via the concepts of ambiguity (or uncertainty) in the sense of Knight (1921) and ambiguity aversion.4 A framework based on ambiguity aversion is appealing to model individual investment decisions. Experimental evidence shows that ambiguity aversion is particularly strong in cases where people feel that their competence in assessing the relevant probabilities is low and in comparative situations (Heath and Tversky (1991) and Fox and Tversky (1995)). Recent experimental evidence in Ahn, Choi, Gale, and Kariv (2010) and Bossaerts, 1 - From Keynes's letter to F. C. Scott, 15 August 1934, Keynes (1983). 2 - Warren Buffett's letter is available at http://www.berkshirehathaway.com/letters/1991.html. 3 - The view of Keynes has been making a comeback also in the field of macroeconomics in the face of the recent financial crisis; see, for example, the article titled "The other-worldly philosophers" in the 3 July 16, 2009 issue of The Economist. 4 - LeRoy and Singell (1987) claim that even the distinction between risk and uncertainty (ambiguity) is made by Keynes (1921) and that Knight (1921) did not intend such a distinction. Ghirardato, Guarnaschelli, and Zame (2010) also shows that investors are averse to ambiguity and that maxmin preferences are a good way to model this behavior. In our model, the investor exhibits different degrees of ambiguity about the distributions of asset returns and considers "familiar" the asset(s) with the lowest level of ambiguity. Specifically, we build on the portfolio selection framework of an ambiguity averse investor developed in Garlappi, Uppal, and Wang (2007). The framework we develop has three attractive features: (i) it is simple and only a mild departure from the well understood Markowitz (1959) model; (ii) it has a solid axiomatic foundation; and (ii) it is capable of capturing in a parsimonious way several aspects of the observed evidence on household portfolios. Our framework can also be thought of as providing an analytic characterization of the concept of familiarity introduced by Huberman (2001). Note that while we use the same modeling framework as Garlappi, Uppal, and Wang (2007), there are several important differences. First, the focus of our work is to provide a positive model in which one can compare the Markowitz and Keynesian views of optimal portfolio selection,
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